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%I #5 Jul 26 2022 11:22:30
%S 1,1,2,6,16,66,246,1248,5976,36120,210480,1479600,10140480,81340560,
%T 640367280,5773662720,51312240000,513773124480,5085768280320,
%U 55995414048000,610811823283200,7334879610643200,87402605773190400
%N Number of deco polyominoes of height n, consisting only of columns of odd length. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
%C a(n)=A121748(n,0).
%D E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F Recurrence relation: a(n)=floor(n/2)(a(n-1)+a(n-2)) for n>=3, a(1)=a(2)=1.
%F D-finite with recurrence +4*a(n) -2*a(n-1) +(-n^2-n+4)*a(n-2) +2*(-n+2)*a(n-3) +(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Jul 26 2022
%e a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes and only the horizontal one consists only of columns of odd length.
%p a[1]:=1: a[2]:=1: for n from 3 to 26 do a[n]:=floor(n/2)*(a[n-1]+a[n-2]) od: seq(a[n],n=1..26);
%Y Cf. A121746, A121748.
%K nonn
%O 1,3
%A _Emeric Deutsch_, Aug 20 2006
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